Salta al contenuto principale
Misurazione aperta

Benchmark

La maggior parte dei software di taglio dichiara una percentuale di resa. Una percentuale non significa nulla senza sapere che cosa era realizzabile — l’80 % può essere ottimale su un lavoro e uno spreco su un altro. Per questo misuriamo invece rispetto al minimo teorico: per ogni lavoro di prova calcoliamo un limite inferiore sul numero di pannelli o barre che qualsiasi piano potrebbe utilizzare, poi indichiamo quanto il nostro piano se ne discosta. Gli input sono istanze accademiche pubblicate, i risultati sono qui sotto, e puoi rieseguire l’intero processo tu stesso.

89,3 %
dei lavori su pannello cadono sul limite o entro un pannello da esso
53,0 %
sono dimostrabilmente ottimali — esattamente sul limite
1,48 %
scarto medio rispetto al limite nei lavori lineari
1259
istanze di prova, 8 insiemi di benchmark

Le cifre sui pannelli sono le 553 istanze canoniche a kerf 0 con rotazione disattivata — la convenzione usata dalla letteratura, così da essere confrontabili con i lavori pubblicati sulle stesse istanze.

Come si calcola il limite

Un limite inferiore è un numero di pannelli sotto il quale nessun piano può scendere. Se il nostro piano lo eguaglia, il piano è dimostrabilmente ottimale per quel lavoro — non ne esiste uno migliore. Si calcolano due limiti e si usa il maggiore; entrambi vengono riportati per ogni lavoro, così da vedere che cosa contribuisce ciascuno.

LB1 — area, corretta per lo spessore della lama (kerf)

Assegna a ogni pezzo posizionato un ingombro ampliato di mezzo kerf su ciascun lato. In uno schema a ghigliottina due pezzi qualsiasi sono separati da almeno un taglio, e ogni taglio consuma un kerf, quindi quegli ingombri non si sovrappongono mai — e stanno tutti all’interno del pannello utile accresciuto di mezzo kerf su ciascun lato. Sommandoli si ottiene un limite che nessuno schema può battere. A kerf 0 questo è il classico limite d’area.

LB1 = ceil( Σ (wᵢ + k)(hᵢ + k) / ((W + k)(H + k)) )

LB2 — funzioni dualmente ammissibili

Il limite d’area è cieco alla forma: cinque pezzi da 600 × 600 usano soltanto l’area di 1.8 pannelli su un pannello da 1000 × 1000, eppure ne entra uno solo per pannello, quindi ne servono cinque. Una funzione dualmente ammissibile è una trasformazione delle dimensioni che preserva l’ammissibilità, e permette all’argomento dell’area di vedere quella struttura. Si usano due famiglie — Martello–Toth e Fekete–Schepers — applicate in modo indipendente a larghezze e altezze, e si prende il miglior risultato sull’intera griglia di parametri. Sotto rotazione a ogni pezzo si imputa la minore delle sue due orientazioni, altrimenti il limite potrebbe superare l’ottimo reale.

LB2 = max over (f,g) of ceil( Σ f(wᵢ + k)·g(hᵢ + k) / (f(W + k)·g(H + k)) )

Perché le istanze vengono scalate

Le istanze pubblicate usano piccoli interi senza unità — alcune hanno un contenitore da 10 × 10. Il nostro algoritmo di posizionamento scarta le strisce libere più sottili di un’unità, che su un contenitore da 10 × 10 sarebbe un decimo del pannello. Ogni istanza viene quindi moltiplicata per un numero intero finché il suo lato corto non raggiunge almeno 1000 unità. Lo scalamento intero è una trasformazione esatta: il numero ottimale di pannelli non cambia, l’istanza si allontana soltanto dalla portata di quella soglia.

Riproducibilità

L’ottimizzatore è deterministico — lo stesso input produce sempre lo stesso piano. L’intero corpus è stato eseguito due volte con la cache disattivata e ogni campo tranne i tempi è tornato identico byte per byte. Le fonti delle istanze sono fissate tramite SHA-256, così una nuova esecuzione può dimostrare di aver misurato gli stessi byte. E ogni lavoro viene verificato rispetto all’invariante secondo cui il limite non supera mai il piano effettivamente prodotto; una sola violazione ferma l’esecuzione anziché pubblicare un numero.

Ciò che questi numeri non dicono

  • Il nostro limite non è il più forte che si conosca. In letteratura esistono limiti più forti, quindi lo scarto che riportiamo è una stima superiore dello scarto reale — un lavoro che segnaliamo come «non sul limite» può in realtà essere ottimale, e semplicemente non possiamo dimostrarlo.
  • Gli scarti relativi si esagerano nei lavori piccoli. Il lavoro mediano qui necessita di circa una dozzina di pannelli, quindi un pannello in più si legge come una percentuale elevata. La colonna assoluta — quanti pannelli oltre il limite — è quella onesta.
  • Due delle famiglie generate sono avverse per costruzione: i loro pezzi ricoprono esattamente i contenitori, senza lasciare alcun margine, quindi qualsiasi imperfezione costa un contenitore intero. Sono una prova di soffitto, non un ritratto del lavoro tipico.
  • Il confine dei 150 pezzi nella tabella delle dimensioni non è arbitrario — è il punto in cui entrambi gli algoritmi di posizionamento cambiano strategia per velocità. I lavori al di sopra seguono un percorso di codice diverso, quindi un cambiamento lì è un compromesso deliberato, non un precipizio.
  • La misurazione richiama le stesse funzioni che esegue la Engine API pubblica, nello stesso processo anziché via HTTP — la latenza di rete corromperebbe i tempi. Questa equivalenza non è data per scontata: un campione di istanze viene rieseguito contro l’API dal vivo e deve tornare identico campo per campo.

Per dimensione del lavoro

Suddiviso per numero di pezzi. Entrambi gli algoritmi di posizionamento abbandonano la loro strategia di ricerca più costosa oltre i 150 pezzi, quindi quel confine separa due percorsi di codice diversi.

PezziLavoriSul limiteScarto medio quando noTempo p95
2D · <5021765,0 %21,0 %23.32 ms
2D · 50-15031547,6 %9,6 %77.34 ms
2D · 150+219,5 %10,1 %474.53 ms
1D · 50-1504835,4 %3,6 %7.12 ms
1D · 150+8633,7 %1,5 %280.55 ms

Che cosa è stato misurato

Due corpora, mai mescolati in un unico numero. Gli insiemi canonici sono le istanze usate dalla letteratura accademica; vengono scaricati e verificati tramite hash anziché copiati qui, perché la loro fonte non dichiara alcuna licenza che ne permetta la ridistribuzione. Gli insiemi generati sono nostri e possiamo pubblicarli.

InsiemeIstanzeOrigineIn questo repository?
CLASS500JSHA-256 9f5ca94d6a…
BENG10MSHA-256 90536b0527…
A43RSHA-256 dd1804179a…
CLASS-R500Generati — costruiti a partire dai parametri del generatore pubblicato, con i nostri semi
PERFECT2D72Generati — costruiti a partire dai parametri del generatore pubblicato, con i nostri semi
UNIF1D40Generati — costruiti a partire dai parametri del generatore pubblicato, con i nostri semi
TRIPLET1D40Generati — costruiti a partire dai parametri del generatore pubblicato, con i nostri semi
RAND1D54Generati — costruiti a partire dai parametri del generatore pubblicato, con i nostri semi

Due famiglie generate portano un ottimo dimostrato per costruzione: i loro pezzi ricoprono esattamente i contenitori con zero sfrido, quindi l’ottimo è noto e non semplicemente limitato.

Gli insiemi di strip-packing, knapsack e packing ortogonale sono esclusi: sono problemi diversi con obiettivi diversi, e per essi una cifra di «contenitori usati» non è definita. La collezione unidimensionale BPPLIB è esclusa per motivi di licenza — i suoi autori la pubblicano sotto CC BY-NC-ND, che non ne permette l’uso nel benchmark di un prodotto commerciale.

Ogni lavoro

Una riga per istanza con le impostazioni principali. Gli altri profili, motori e orientazioni sono nel file dei risultati scaricabile.

Mostrati 1259 di 1259

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PERFECT2D/p_300x300_k3_n8_2PERFECT2D241200×120034+1756.11
PERFECT2D/p_300x300_k3_n16_1PERFECT2D481200×120034+17518.53
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PERFECT2D/p_300x300_k3_n30_1PERFECT2D901200×120034+17546.08
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PERFECT2D/p_300x300_k5_n8_2PERFECT2D401200×120056+183.3313.62
PERFECT2D/p_300x300_k5_n16_1PERFECT2D801200×120056+183.3331.67
PERFECT2D/p_300x300_k5_n16_2PERFECT2D801200×120056+183.3329.66
PERFECT2D/p_300x300_k5_n30_1PERFECT2D1501200×120056+183.3394.05
PERFECT2D/p_300x300_k5_n30_2PERFECT2D1501200×120056+183.3396.34
UNIF1D/u120_01UNIF1D1201050474798.757.75
UNIF1D/u120_02UNIF1D12010504849+197.655.49
UNIF1D/u120_03UNIF1D12010504849+196.754.99
UNIF1D/u120_04UNIF1D1201050525298.1711.44
UNIF1D/u120_05UNIF1D1201050515198.074.13
UNIF1D/u120_06UNIF1D12010505052+295.914.52
UNIF1D/u120_07UNIF1D12010505152+198.054.68
UNIF1D/u120_08UNIF1D12010504950+197.434.14
UNIF1D/u120_09UNIF1D12010505152+196.824.76
UNIF1D/u120_10UNIF1D1201050454598.434.42
UNIF1D/u250_01UNIF1D250105099101+297.919.47
UNIF1D/u250_02UNIF1D2501050102104+297.5318.79
UNIF1D/u250_03UNIF1D2501050959599.1619.77
UNIF1D/u250_04UNIF1D2501050102103+198.5222.85
UNIF1D/u250_05UNIF1D2501050104106+298.0919.32
UNIF1D/u250_06UNIF1D2501050101103+297.6119.05
UNIF1D/u250_07UNIF1D250105010010099.2516.68
UNIF1D/u250_08UNIF1D2501050105106+198.4118.45
UNIF1D/u250_09UNIF1D2501050102103+198.4321.17
UNIF1D/u250_10UNIF1D250105098100+297.6118.34
UNIF1D/u500_01UNIF1D5001050199200+199.4479.63
UNIF1D/u500_02UNIF1D500105019619699.9480.92
UNIF1D/u500_03UNIF1D5001050204206+298.6379.14
UNIF1D/u500_04UNIF1D5001050196198+298.9579.26
UNIF1D/u500_05UNIF1D500105019919999.6778.27
UNIF1D/u500_06UNIF1D500105020420499.7279.14
UNIF1D/u500_07UNIF1D5001050202205+398.5378.48
UNIF1D/u500_08UNIF1D5001050200202+298.5979
UNIF1D/u500_09UNIF1D500105020020099.7474
UNIF1D/u500_10UNIF1D500105019719799.776.38
UNIF1D/u1000_01UNIF1D1000105040340399.96292.33
UNIF1D/u1000_02UNIF1D10001050398399+199.52309.11
UNIF1D/u1000_03UNIF1D1000105040140199.95303.68
UNIF1D/u1000_04UNIF1D10001050392393+199.66280.55
UNIF1D/u1000_05UNIF1D10001050399400+199.73280.16
UNIF1D/u1000_06UNIF1D10001050403404+199.63278.34
UNIF1D/u1000_07UNIF1D10001050409410+199.65295.87
UNIF1D/u1000_08UNIF1D1000105039839899.85277.36
UNIF1D/u1000_09UNIF1D1000105039939999.98279.3
UNIF1D/u1000_10UNIF1D10001050403405+299.42271.44
TRIPLET1D/t60_01TRIPLET1D6010002021+195.247.12
TRIPLET1D/t60_02TRIPLET1D6010002021+195.240.87
TRIPLET1D/t60_03TRIPLET1D6010002021+195.240.89
TRIPLET1D/t60_04TRIPLET1D6010002021+195.240.84
TRIPLET1D/t60_05TRIPLET1D6010002021+195.241.14
TRIPLET1D/t60_06TRIPLET1D6010002021+195.240.92
TRIPLET1D/t60_07TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_08TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_09TRIPLET1D6010002021+195.240.82
TRIPLET1D/t60_10TRIPLET1D6010002021+195.240.82
TRIPLET1D/t120_01TRIPLET1D12010004041+197.562.92
TRIPLET1D/t120_02TRIPLET1D12010004041+197.563.01
TRIPLET1D/t120_03TRIPLET1D12010004041+197.562.96
TRIPLET1D/t120_04TRIPLET1D12010004041+197.563.32
TRIPLET1D/t120_05TRIPLET1D12010004041+197.563.23
TRIPLET1D/t120_06TRIPLET1D12010004041+197.562.88
TRIPLET1D/t120_07TRIPLET1D12010004041+197.563
TRIPLET1D/t120_08TRIPLET1D12010004041+197.562.9
TRIPLET1D/t120_09TRIPLET1D12010004041+197.563.34
TRIPLET1D/t120_10TRIPLET1D12010004041+197.562.91
TRIPLET1D/t249_01TRIPLET1D24910008386+396.5116.84
TRIPLET1D/t249_02TRIPLET1D24910008384+198.8111.79
TRIPLET1D/t249_03TRIPLET1D24910008385+297.6512.07
TRIPLET1D/t249_04TRIPLET1D24910008386+396.5118.21
TRIPLET1D/t249_05TRIPLET1D24910008385+297.6512.73
TRIPLET1D/t249_06TRIPLET1D24910008385+297.6512.29
TRIPLET1D/t249_07TRIPLET1D24910008385+297.6512.18
TRIPLET1D/t249_08TRIPLET1D24910008385+297.6512.11
TRIPLET1D/t249_09TRIPLET1D24910008385+297.6512.01
TRIPLET1D/t249_10TRIPLET1D24910008385+297.6511.76
TRIPLET1D/t501_01TRIPLET1D5011000167171+497.6653.07
TRIPLET1D/t501_02TRIPLET1D5011000167171+497.6646.74
TRIPLET1D/t501_03TRIPLET1D5011000167171+497.6646.6
TRIPLET1D/t501_04TRIPLET1D5011000167171+497.6651.66
TRIPLET1D/t501_05TRIPLET1D5011000167171+497.6655.78
TRIPLET1D/t501_06TRIPLET1D5011000167170+398.2455.08
TRIPLET1D/t501_07TRIPLET1D5011000167171+497.6652.44
TRIPLET1D/t501_08TRIPLET1D5011000167171+497.6646.9
TRIPLET1D/t501_09TRIPLET1D5011000167171+497.6646.52
TRIPLET1D/t501_10TRIPLET1D5011000167171+497.6654.43
RAND1D/r_50_100_0.1_0.7_1RAND1D5010002122+194.593.18
RAND1D/r_50_100_0.1_0.7_2RAND1D501000212196.571.62
RAND1D/r_50_100_0.1_0.7_3RAND1D5010002020971.49
RAND1D/r_50_100_0.2_0.8_1RAND1D501000282890.611.49
RAND1D/r_50_100_0.2_0.8_2RAND1D5010002626931.39
RAND1D/r_50_100_0.2_0.8_3RAND1D5010002324+194.631.4
RAND1D/r_50_150_0.1_0.7_1RAND1D501050202095.831.53
RAND1D/r_50_150_0.1_0.7_2RAND1D501050202095.631.39
RAND1D/r_50_150_0.1_0.7_3RAND1D5010502223+194.71.5
RAND1D/r_50_150_0.2_0.8_1RAND1D501050313180.691.63
RAND1D/r_50_150_0.2_0.8_2RAND1D501050303085.185.51
RAND1D/r_50_150_0.2_0.8_3RAND1D501050252595.761.23
RAND1D/r_50_1000_0.1_0.7_1RAND1D5010002122+193.10.68
RAND1D/r_50_1000_0.1_0.7_2RAND1D5010002021+194.890.63
RAND1D/r_50_1000_0.1_0.7_3RAND1D501000212196.710.67
RAND1D/r_50_1000_0.2_0.8_1RAND1D501000292988.750.71
RAND1D/r_50_1000_0.2_0.8_2RAND1D501000303089.930.71
RAND1D/r_50_1000_0.2_0.8_3RAND1D501000282891.310.64
RAND1D/r_200_100_0.1_0.7_1RAND1D20010007879+197.759.76
RAND1D/r_200_100_0.1_0.7_2RAND1D20010007879+198.6211.04
RAND1D/r_200_100_0.1_0.7_3RAND1D2001000828298.9911.08
RAND1D/r_200_100_0.2_0.8_1RAND1D200100010110198.1914.01
RAND1D/r_200_100_0.2_0.8_2RAND1D200100011011092.949.21
RAND1D/r_200_100_0.2_0.8_3RAND1D200100010810894.889.27
RAND1D/r_200_150_0.1_0.7_1RAND1D2001050828298.8510.62
RAND1D/r_200_150_0.1_0.7_2RAND1D20010507778+198.3610.73
RAND1D/r_200_150_0.1_0.7_3RAND1D20010508081+198.219.84
RAND1D/r_200_150_0.2_0.8_1RAND1D200105010010097.079.6
RAND1D/r_200_150_0.2_0.8_2RAND1D2001050101102+196.9314.27
RAND1D/r_200_150_0.2_0.8_3RAND1D200105010010098.069.41
RAND1D/r_200_1000_0.1_0.7_1RAND1D20010008485+198.489.5
RAND1D/r_200_1000_0.1_0.7_2RAND1D20010007677+198.029.56
RAND1D/r_200_1000_0.1_0.7_3RAND1D20010008081+197.859.03
RAND1D/r_200_1000_0.2_0.8_1RAND1D20010009899+198.158.85
RAND1D/r_200_1000_0.2_0.8_2RAND1D200100010610695.248.67
RAND1D/r_200_1000_0.2_0.8_3RAND1D200100010810894.29.4
RAND1D/r_500_100_0.1_0.7_1RAND1D5001000196197+199.3264.83
RAND1D/r_500_100_0.1_0.7_2RAND1D500100020420499.969.21
RAND1D/r_500_100_0.1_0.7_3RAND1D500100020020099.6970.26
RAND1D/r_500_100_0.2_0.8_1RAND1D5001000263264+196.4362.33
RAND1D/r_500_100_0.2_0.8_2RAND1D5001000249250+198.5462.99
RAND1D/r_500_100_0.2_0.8_3RAND1D500100025625697.5364.82
RAND1D/r_500_150_0.1_0.7_1RAND1D500105020220299.8971.84
RAND1D/r_500_150_0.1_0.7_2RAND1D500105020420499.6573.46
RAND1D/r_500_150_0.1_0.7_3RAND1D500105019219299.7575.24
RAND1D/r_500_150_0.2_0.8_1RAND1D500105026126196.7264.54
RAND1D/r_500_150_0.2_0.8_2RAND1D500105025025098.8764.97
RAND1D/r_500_150_0.2_0.8_3RAND1D500105027027095.2663.52
RAND1D/r_500_1000_0.1_0.7_1RAND1D5001000194196+298.6659.23
RAND1D/r_500_1000_0.1_0.7_2RAND1D5001000198201+398.4462.32
RAND1D/r_500_1000_0.1_0.7_3RAND1D5001000199200+199.0957.15
RAND1D/r_500_1000_0.2_0.8_1RAND1D5001000260261+196.9264.69
RAND1D/r_500_1000_0.2_0.8_2RAND1D5001000261262+196.262.77
RAND1D/r_500_1000_0.2_0.8_3RAND1D5001000259262+396.3258.46

Nesting a forma reale

I numeri qui sopra sono del packer a ghigliottina, che taglia rettangoli. Il nesting a forma reale è un motore diverso per un problema diverso: dispone POLIGONI ARBITRARI — per taglio laser, plasma e getto d’acqua — facendo incastrare i pezzi nelle tasche concave gli uni degli altri. Su un lavoro rappresentativo da 272 pezzi usa 6 lastre, là dove gli stessi identici pezzi passati a un packer rettangolare tramite il loro bounding box ne richiedono 9 — un terzo di materiale in meno, solo grazie alla forma.

6
lastre · forma reale
5
lastre · motore max, 60 s
9
lastre · bounding box
4
lastre · minimo teorico

Perché riportiamo il numero di lastre, non la densità

Un packer a bounding box conta l’aria degli intagli dentro il rettangolo di ogni pezzo come piena, quindi la sua «resa» appare più alta per un risultato peggiore — il piano da 9 lastre sembra più denso di quello da 6. L’unica metrica onesta e confrontabile è il numero di lastre di cui gli stessi pezzi fisici hanno realmente bisogno. È il numero qui sopra.

Il piano da 6 lastre è il motore predefinito veloce, che risponde nella stessa richiesta. Il motore asincrono max (engine:"max") continua poi a cercare meno lastre: misurato sul nostro server di produzione il 22 settembre 2026, ha usato 5 lastre su 4 esecuzioni con il suo budget predefinito di 60 secondi, e 5 su 2 esecuzioni con il massimo di 180 secondi. È limitato nel tempo, quindi un’esecuzione può concludersi diversamente da un’altra — mostriamo l’intervallo su tutte le esecuzioni, non la migliore. Ogni schema è stato verificato in modo indipendente: ogni pezzo posizionato e sulla propria lastra, con non più di 0,01 mm di sovrapposizione tra due pezzi — un margine per le coordinate arrotondate restituite dall’API, perché pezzi che si toccano possono altrimenti sembrare incrociarsi di pochi millesimi di millimetro.

Un limite inferiore teorico su questo lavoro è 4 lastre — l’area totale dei pezzi divisa per una lastra. Nessun piano può usarne meno; con forme irregolari, l’aria tra i pezzi fa sì che un piano lo raggiunga raramente.

Quelle cifre non hanno alcuno spazio tra i pezzi. Con uno spazio di 5 mm tra i pezzi e verso il bordo della lastra, un’impostazione laser comune, lo stesso lavoro richiede 6 lastre con il motore predefinito e 5–6 con max (2 esecuzioni, 60 s ciascuna).

I classici insiemi di nesting ESICUP

Il lavoro qui sopra è uno che abbiamo costruito noi. Per poter verificare il motore anche su problemi che non abbiamo scelto, lo abbiamo eseguito sui 13 classici insiemi di nesting ESICUP, le istanze pubbliche di packing irregolare usate dalla letteratura di ricerca. Sono problemi di strip-packing; li trasformiamo in problemi su lastre come fa la letteratura sul bin-packing, con tre dimensioni di lastra quadrata per insieme, il che dà 39 istanze. Su tutte queste il motore predefinito usa 248 lastre e il motore max 244 (la peggiore di 2 esecuzioni, 60 s ciascuna), contro un limite inferiore di 153. Il motore predefinito raggiunge il limite su 7 istanze e max su 11. Max richiede meno lastre del motore predefinito su 4 istanze, in ogni esecuzione.

Come è stato misurato, sul nostro server di produzione il 22 settembre 2026: ogni lastra è un quadrato il cui lato è 1,1, 1,5 o 2 volte la dimensione massima del pezzo (la convenzione di Martinez-Sykora et al., 2017); ogni insieme mantiene le proprie rotazioni consentite; non c’è alcuno spazio tra i pezzi, come in letteratura; max viene eseguito con il suo budget predefinito di 60 secondi e riportiamo la sua esecuzione peggiore. Il limite inferiore, l’area totale dei pezzi divisa per una lastra, è debole per le forme irregolari, quindi un risultato al di sopra di esso non è necessariamente battuto da nulla. Ogni schema è stato verificato al di fuori del motore: 39 istanze su 39 sono valide, con ogni pezzo posizionato sulla propria lastra e nessuna coppia di pezzi sovrapposta oltre l’arrotondamento delle coordinate restituite. Le istanze provengono dal repository jagua-rs, nella revisione da cui è costruito il nostro motore (la collezione ESICUP è sotto CC0), e lo script che le ha misurate si trova nel nostro repository.

Tutte le 39 istanze
InsiemeLato della lastra (× pezzo più grande)PezziLimite inferiorePredefinitoMax · 60 s
albano1,124466
albano1,524333
albano224222
blaz11,128112020
blaz11,52861414
blaz1228466
dagli1,130344
dagli1,530222
dagli230111
fu1,112599
fu1,512355
fu212232
jakobs11,125699
jakobs11,525344
jakobs1225233
jakobs21,125588
jakobs21,525344
jakobs2225232
mao1,120344
mao1,520232
mao220121
marques1,124466
marques1,524333
marques224222
shapes01,14371717
shapes01,54341010
shapes0243355
shapes11,14371515
shapes11,543488
shapes1243344
shirts1,199111616
shirts1,599699
shirts299455
swim1,14861212
swim1,548466
swim248233
trousers1,164566
trousers1,564344
trousers264222

Risultati per istanza (JSON)

Nesting a forma reale sull’Engine API →

The max tier — closer to the proven optimum

The figures above are the default engine, which returns instantly. The optional async max engine (engine:"max") runs a tree search instead: on the same public 2DPackLib instances, judged by the same lower bound, it reaches the PROVEN minimum on 12–13 percentage points more jobs than the default, with a smaller gap on the ones that miss. The trade is time — see below.

CorpusEngineOn the boundAvg gap (off-bound)
A + BENG · 106default · heuristic44,3 %11,1 %
max · PackingSolver57,1 %6,9 %
CLASS (sample) · 168default · heuristic57,7 %12,8 %
max · PackingSolver69,6 %10,4 %

Why the max tier is asynchronous

The default engine solves in about 30 ms and runs in your browser. The max engine takes seconds to a minute per job — too long to hold an HTTP request open — so it is asynchronous: POST with engine:"max" returns a job id, and you poll until it finishes. Same public corpus, same lower-bound method, both our own engines — no competitor data.

One honest caveat: the max engine is time-boxed, so on the very hardest instances the search is cut off at the cap — a few jobs may not finish (1 of 274 here) and its figures can move by about a point between runs. The default engine is fully deterministic and always returns a plan.

The max tier on the Engine API →

Dati

La misurazione completa, non un suo riassunto.

  • results.jsonl — Tutti i risultati — ogni lavoro, profilo, motore e orientazione
  • summary.json — Aggregati — i numeri di questa pagina
  • table.json — Questa tabella in JSON
  • corpus.json — Le istanze di input generate — i problemi reali che l’esecutore ha risolto. Gli insiemi accademici canonici vengono ottenuti e verificati tramite hash anziché copiati qui, perché la loro fonte non concede la ridistribuzione.

Per riprodurre: clona il repository, esegui npm run bench:fetch per scaricare le istanze canoniche e verificarne gli hash, poi npm run bench. Il corpus generato non necessita di download.

I file qui sopra sono pubblicati sotto CC BY 4.0 — riutilizzali, uso commerciale incluso, con attribuzione a CutOptim. Questo copre la nostra misurazione e il corpus generato. Le istanze accademiche canoniche non sono nostre da concedere in licenza e non vengono distribuite da qui.

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